Frequency modulation synthesis

**FM synthesis using 2 operators**
A 220 Hz carrier tone f_c modulated by a 440 Hz modulating tone f_m, with various choices of frequency modulation index, β. The time domain signals are illustrated above, and the corresponding spectra are shown below (spectrum amplitudes in dB).
Waveforms for each β
Spectra for each β

Frequency modulation synthesis (or FM synthesis) is a form of sound synthesis whereby the frequency of a waveform is changed by modulating its frequency with a modulator. The (instantaneous) frequency of an oscillator is altered in accordance with the amplitude of a modulating signal.^[1]

FM synthesis can create both harmonic and inharmonic sounds. To synthesize harmonic sounds, the modulating signal must have a harmonic relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively complex. Through the use of modulators with frequencies that are non-integer multiples of the carrier signal (i.e. inharmonic), inharmonic bell-like and percussive spectra can be created.

FM synthesis using analog oscillators may result in pitch instability.^[2] However, FM synthesis can also be implemented digitally, which is more stable and became standard practice.

^ Dodge & Jerse 1997, p. 115
^ McGuire, Sam; Matějů, Zbyněk (2020-12-28). The Art of Digital Orchestration. CRC Press. ISBN 978-1-000-28699-1.

[1] Dodge & Jerse 1997, p. 115

[2] McGuire, Sam; Matějů, Zbyněk (2020-12-28). The Art of Digital Orchestration. CRC Press. ISBN 978-1-000-28699-1.

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